Mexico's economy minister said that he saw diminishing chances for a new North American Free Trade Agreement ahead of a Thursday deadline to present a deal that could be signed by the current U.S. Congress.

U.S. House Speaker Paul Ryan has said that the Republican-controlled Congress would need to be notified of a new NAFTA deal by Thursday to give lawmakers a chance of approving it before a newly elected Congress takes over in January.

"It is not easy. We do not think we will have it by Thursday," Mexican Economy Minister Ildefonso Guajardo told broadcaster Televisa on Tuesday.

But Canadian Prime Minister Justin Trudeau struck a more upbeat tone, telling reporters in Calgary a few hours later, "There is very much an eminently achievable outcome ... and we are very close."

"We are going to continue to remain optimistic," said Trudeau. He met with U.S. President Donald Trump on Monday and discussed the possibility of bringing NAFTA talks to a "prompt conclusion."

Negotiators from the United States, Mexico and Canada have been in intense talks since last month to try to reach a deal before U.S. congressional elections in November. Mexico's presidential vote on July 1 also complicates the process.

"We will keep negotiating, and in the moment that we have a good negotiation, we can close the deal ... independent of which Congress (the current or new) that will vote on it," said Guajardo.

Mexico's peso sank to its weakest level in over a year on Tuesday, and the country's benchmark stock index fell about 1 percent to its lowest since early April.

Guajardo said the talks could be concluded before or just after the July 1 vote.

Leftist Andres Manuel Lopez Obrador is leading polls to win the presidential race, and his pick for economy minister, Graciela Marquez, said last month his administration would be willing to accept a deal struck before the election.

If that is not possible, she said it would be better to complete the negotiation after the next government takes office at the start of December. Guajardo said the next government's team would need to be involved in any talks after July 1.

Guajardo said negotiators were getting close to reaching a deal on rules for the auto sector under NAFTA.

However, talks still faced the hurdles of U.S. demands for a sunset clause that would allow NAFTA to expire if it is not renegotiated every five years, and the elimination of settlement panels for trade disputes.

More flexibility was needed for a deal, Guajardo said.

Kenneth Smith, the chief Mexican negotiator at the talks, said that for Mexico there were no deadlines.

Irrespective of the Thursday deadline mentioned by Ryan, there was still time to ratify a new NAFTA this year, Smith told broadcaster Enfoque Noticias.

Hanging over the talks is Trump's threat to impose steel and aluminum tariffs on its trade partners. Mexico and Canada have been spared so far, although the latest exemption for them will run out at the end of May.

Smith said his government would retaliate with equivalent measures "immediately" if tariffs or quotas were imposed.